
For checking purposes we explicitly write out the terms up to order \(\varepsilon \)  and
confirm that it exactly coincides with result derived
before in Refs. [1]}, [2]}, [3]}:
\(I_{1,1}^{(0)}(v_{12},\varepsilon )=\pi \left(\frac{v_{12}}{2}\right)^{-1-\varepsilon }\left[-\frac{1}{\varepsilon }-\varepsilon \,\mathrm {Li}_2\left(1-\frac{v_{12}}{2}\right)+\mathcal {O}(\varepsilon ^2)\right]\,.\) 
